Let w = 4x ^2 + 4y ^2 + z ^2 , x = ? sin ? cos ? , y = ? sin ? sin ? , z = ? cos

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Let w = 4x ^2 + 4y ^2 + z ^2 , x = ? sin ? cos ? , y = ? sin ? sin ? , z = ? cos ?. Find?w /??, ?w /??, and ?w / ?? .
Copyright | Wiley | Calculus | julanars@yahoo.com | Printed from Chegg iOS App Let w = 4x ^2 + 4y ^2 + z ^2 , x = ? sin ? cos ? , y = ? sin ? sin ? , z = ? cos ?. Find?w /??, ?w /??, and ?w / ?? .
Copyright | Wiley | Calculus | julanars@yahoo.com | Printed from Chegg iOS App Let w = 4x ^2 + 4y ^2 + z ^2 , x = ? sin ? cos ? , y = ? sin ? sin ? , z = ? cos ?. Find?w /??, ?w /??, and ?w / ?? .
Copyright | Wiley | Calculus | julanars@yahoo.com | Printed from Chegg iOS App

Explanation / Answer

Just apply chain rule for diffrentiation

?w /?? = 8x*sin ? cos ?+ 8y*sin ? sin ? + 2z*cos ?

?w /??= ?* (8x*cos ? cos ?+ 8y*cos ? sin ? - 2z*sin ?)

?w / ?? = ?* (- 8x*sin ? sin ?+ 8y*sin ? cos ?)

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Let w = 4x ^2 + 4y ^2 + z ^2 , x = ? sin ? cos ? , y = ? sin ? sin ? , z = ? cos

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